It is common for students with fairly good math grades to score poorly on the SAT math section. This happens because the standard math curriculum is more about following directions than about understanding concepts or solving problems, and the SAT is the opposite.
In my opinion, the ability to solve problems is the true measure of progress in math. Most math classes do not develop, or even attempt to develop, this ability except in very limited contexts (one or two chapters at a time).
Why don’t the schools improve their curriculum? There are several reasons:
- Teachers are not free to make the necessary changes.
- A curriculum based on problem solving is not well suited to the usual ways of teaching, testing, and grading.
- It takes a lot of time and effort to develop a thorough understanding of math. This is true even of such basic concepts as fractions and decimals. Schools have decided that everyone needs to learn math up to Algebra 2, but most people are unable or unwilling to do so. To maintain a pretense that students are learning math, they are taught to manipulate numbers and graphs in ways that can be done with minimal understanding.
More on the mainstream math program and how it can be improved:
The Teaching of Arithmetic by L.P. Benezet
Mathematical Education, by William P. Thurston
Assessing True Academic Success, by Dan Kennedy
I offer tutoring for all ages in math problem solving. I have a large collection of problems to draw from — problems that require the depth of thought that develops true mastery of math concepts. I can also provide math problems for students to take home and work at their own pace.
This is especially worthwhile in grades 6 to 10, or from pre-algebra to algebra 2, because there is so much more depth to the material than math classes generally cover. Also, several topics such as fractions, decimals, percent, and proportions need to be revisited throughout these years in order to be mastered.